Laguere’s Method and a Circle which Contains at Least One Zero of a Polynomial

Autor:	W. Kahan
Rok vydání:	1967
Předmět:	Polynomial (hyperelastic model) Numerical Analysis Sequence Mathematics::Commutative Algebra Applied Mathematics Zero (complex analysis) Combinatorics Computational Mathematics Laguerre polynomials Degree of a polynomial Constant (mathematics) Complex number Square number Mathematics
Zdroj:	SIAM Journal on Numerical Analysis. 4:474-482
ISSN:	1095-7170 0036-1429
DOI:	10.1137/0704042
Popis:	Given an Nth degree polynomial $P(z)$ one may use Laguerre’s method to generate a sequence of complex numbers $x_0 ,x_1 ,x_2 , \ldots $ which usually converges to a, zero of $P(z)$. This note shows that each circle $\left| {z - x_n } \right| \leqq \sqrt N \left| {x_{n + 1} - x_n } \right|$ contains at least one zero of $P(z)$. If N is not a perfect square, then the constant $\sqrt N $ can be replaced by a slightly smaller constant $R_N $.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8a86bc36f25d6792f827611f660b8c53 https://doi.org/10.1137/0704042 Zobrazit plný text záznamu